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The concepts of necessary and sufficient conditions help us understand and explain the different kinds of connections between concepts, and how different states of affairs are related to each other.
To say that X is a necessary condition for Y is to say that it is impossible to have Y without X. In other words, the absence of X guarantees the absence of Y. A necessary condition is sometimes also called "an essential condition". Some examples :
To show that X is not a necessary condition for Y, we simply find a situation where Y is present but X is not. Examples :
Additional remarks about necessary conditions :
To say that X is a sufficient condition for Y is to say that the presence of X guarantees the presence of Y. In other words, it is impossible to have X without Y. If X is present, then Y must also be present. Again, some examples :
To show that X is not sufficient for Y, we come up with cases where X is present but Y is not. Examples :
Additional remarks about sufficient conditions :
Given two conditions X and Y, there are four ways in which they might be related to each other:
Rewrite these claims in terms of necessary and / or sufficient conditions :
(a) You must pay if you want to enter.Payment is necessary for entrance
(b) A cloud chamber is needed to observe subatomic particles.A cloud chamber is necessary for observing subatomic particles.
(c) If something is an electron it is a charged particle.Being an electron is sufficient for being a charged particle.
(d) I will pay for lunch if and only if you pay for dinner.My paying for lunch is necessary and sufficient for your paying for dinner.
Question 2.Suppose Tom is a tall but unsuccessful person. Does it show that (a) being tall is not sufficient for being successful, or (b) being tall is not necessary for being successful?
Discuss how these conditions are related to each other and explain your answers :
(a) not being poor, being richThe first is necessary but not sufficient for the second, since it is possible to be neither poor nor rich.
(b) being an even number, being divisible by 2The first is both necessary and sufficient for the second.
(c) being an intelligent student, being the most intelligent studentNeither necessary nor sufficient. Why?
(d) having ten dollars, having more than five dollarsThe first is sufficient but not necessary for the second.
(e) the presence of the rule of law, being a just societyThis is a difficult one!
(f) giving money to another person in exchange for a favour, corruption
(g) taking place on a weekday, not being held on Saturday
Bertrand Arthur William Russell